RCMP Const. Kris Clark said the 55-year-old male victim died on the bus early Thursday evening.
"According to witnesses, as the male suspect left the bus he made a shoving motion towards the victim," Clark said. "The victim was found immediately after suffering from a serious injury which resulted in his death."
Clark said a police service dog was on the scene and quickly established a trail but the suspect was not located.
Supt. Nick Romanchuk said he understands that the crime is disturbing to the community.
"I would like to assure the public that all resources needed for the investigation are currently in place and every effort is being made to identify and apprehend the suspect as soon as possible," he said Friday.
Romanchuk urged anyone with information that may identify the suspect to call police.
Les Milton, president of the Kelowna local of the Amalgamated Transit Workers union, said it was a rough night for passengers and the bus driver.
The passenger is believed to have been stabbed in the neck when the bus pulled over at a regular stop, Milton said.
BC Transit and its operating company FirstCanada ULC "are deeply saddened by this violent and tragic attack," Transit spokeswoman Maribeth Burton said.
"All 10 passengers who were on the bus were driven home by transit staff after police finished interviewing them, which was over a two-and-a-half-hour period," she said.
"As you might imagine, our operator is off today and he is deeply disturbed by last night's tragedy."
All transit staff in Kelowna have been offered counselling, Burton said, and the company is urging anyone with information to call police.
She said BC Transit hopes to begin installing surveillance cameras on its fleet by next year.
A man who stabbed and beheaded a passenger aboard a Greyhound bus in Manitoba six years ago was later found not criminally responsible due to a mental illness. (The Canadian Press, CKFR)